1. Sept. 14 th 2004 Montauk, Long Island, NY Jason S. Gardner NIST, Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899-8562 Department of Physics, Brookhaven National Laboratory, Upton, NY 11973-5000. Neutron Scattering Studies of Magnetically Frustrated Pyrochlores

2. Pyrochlore Lattice ?

3. Diffuse Scattering (0,0,l) (h,h,0) Tb 2 Ti 2 O 7 JS Gardner et al., Phys. Rev. B 64, 224416 (2001). Y 2 Mo 2 O 7 J S Gardner et al., Phys. Rev. Lett., 83, 211 (1999). Ho 2 Ti 2 O 7 ST Bramwell et al. PRL 87, 047205 (2001). S.-H. Lee et al. Nature 418, 856 (2002)

4. Outline Spin dynamics Spin dynamics 3 Compounds 3 Compounds Antiferromagnetic frustrated systems Antiferromagnetic frustrated systems –Yb 2 Ti 2 O 7, Gd 2 Ti 2 O 7 »Strange dynamics and partial ordering Ferromagnetic frustrated systems Ferromagnetic frustrated systems –Ho 2 Ti 2 O 7 »Spin Ice (Uniquely frozen)

5. Sept. 14 th 2004 Montauk, Long Island, NY Spin Echo Principle I(Q,t) = I S(Q,  )cos(  t)d  Cosine transform

6. New Spectrometer

7. Typical Magnetic Neutron Spin Echo 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0.010.11 25.0K 22.5K 18.9K 10.0K S(Q,t)/S(Q,0) Time (ns) 50 % 0.009 0.01 0.011 0.012 0.013 0.014 0.015 510152025303540 M/H (emu/mol) Temperature (K) 22.5 K ZFC FC

8. Sept. 14 th 2004 Montauk, Long Island, NY Spin Ice

9. FM Spin Ices – RE 2 Ti 2 O 7 (Ho and Dy) K. Matsuhira et al., J. Phys.: Condens. Matter 12 (2000) L649–L656 and 13 (2001) L737-L746 Ho 2 Ti 2 O 7

10. FM Spin Ice

11. Correlation J Snyder et al. PRB 69 064414 (2004) Mag (arb. units) Ho 2 Ti 2 O 7 Dy 2 Ti 2 O 7

12. Spin Echo Results

13. New Spectrometer New territory

14. New Data

15. Sept. 14 th 2004 Montauk, Long Island, NY Partial Order Gd 2 Ti 2 O 7 -- ½ filled orbital -- Experimental realisation of a Heisenberg spin on a pyrochlore lattice -- found to order???? -- very anisotropic??

16. Gd 2 Ti 2 O 7 - Partially ordered A. P. Ramirez, et al.. Rev. Lett. 89, 067202 (2002) 1.1K 0.7K

17. Powder diffraction

18. Magnetic Structure 1k 4k

19. NPD (Champion et al. Rev. B 64, 140407 (2001)) Kagome Planes INTERSTITIAL SITE ∑ = 0 N=1 ∞

20. 0.77 K Transition

21. 50 mK Structure 1k 4k RED circles BLUE balls

22. 0.77 K Transition

23. What else do we know…. A. P. Ramirez, et al.. Rev. Lett. 89, 067202 (2002) (000) (½½½)

24. Neutron Spin Echo (preliminary results) ¾ ¼ T > 1K Entire spin system is inelastic and T < 1K 25% of the spin system is static REM: NPD revealed 75% of the system is static below the 1 st transition; At all T, NSE fits results in a S(Q,t)/S(q,0) as t  0 of 75%.

25. Sept. 14 th 2004 Montauk, Long Island, NY More Unusual Magnetism -Yb 2 Ti 2 O 7

26. Yb 2 Ti 2 O 7

27. New Data

28. Conclusions 6 6 Exotic Magnetic Order 6 6 Large moment systems 6 6 Big crystals   NSE ideal time (  ) window

29. Sept. 14 th 2004 Montauk, Long Island, NY Collaborators G Ehlers (SNS) A Cornelius (UNLV) R Stewart (ILL) S Bramwell, A Wills and T Fennell(UCL) Nick Rosov (NIST)